Question

# In the system shown, mass of block A, B and C are mA=4m, mB=3m and mC=8m. If the system is released from rest, find the acceleration of block B. Assume all surfaces to be smooth and string inextensible.

A
g8
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
g2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
g4
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
g
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B g2Let the given system is reframed as shown So, from the FBDs of A,B and C, we get T=3maB ... (1) In vertical direction: 4mg−T=4maA ... (2) In horizontal direction: N2−N1=4maC ... (3) N1+T−N2=8maC ... (4) From constrained condition, using method of intercept we have ..L1+..L2=0⇒aA−aC−aB=0 aA=aC+aB ... (5) Adding eq (2) and (3), we get, 4mg−T+N2−N1=4m(aA+aC) Using eq. (4), we get 4mg−8maC=4m(aA+aC) ⇒4mg=4m(aA+aC+2aC) ⇒aA+3aC=g ... (6) From (3) & (4), we get T=12maC ... (7) From (1) & (7) we have, 3maB=12maC⇒aB=4aC ... (8) From (5), (6) & (7) we have, g−3aC=aC+4aC⇒aC=g8⇒aB=g2

Suggest Corrections
12
Join BYJU'S Learning Program
Related Videos
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program